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Simplifying (0.1x + -0.3)(0.4x + -20) = 0 Reorder the terms: (-0.3 + 0.1x)(0.4x + -20) = 0 Reorder the terms: (-0.3 + 0.1x)(-20 + 0.4x) = 0 Multiply (-0.3 + 0.1x) * (-20 + 0.4x) (-0.3(-20 + 0.4x) + 0.1x * (-20 + 0.4x)) = 0 ((-20 * -0.3 + 0.4x * -0.3) + 0.1x * (-20 + 0.4x)) = 0 ((6 + -0.12x) + 0.1x * (-20 + 0.4x)) = 0 (6 + -0.12x + (-20 * 0.1x + 0.4x * 0.1x)) = 0 (6 + -0.12x + (-2x + 0.04x2)) = 0 Combine like terms: -0.12x + -2x = -2.12x (6 + -2.12x + 0.04x2) = 0 Solving 6 + -2.12x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 150 + -53x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -53x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -53x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -53x + x2 = 0 + -150 -53x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -53x + x2 = -150 The x term is -53x. Take half its coefficient (-26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. -53x + 702.25 + x2 = -150 + 702.25 Reorder the terms: 702.25 + -53x + x2 = -150 + 702.25 Combine like terms: -150 + 702.25 = 552.25 702.25 + -53x + x2 = 552.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 552.25 Calculate the square root of the right side: 23.5 Break this problem into two subproblems by setting (x + -26.5) equal to 23.5 and -23.5.Subproblem 1
x + -26.5 = 23.5 Simplifying x + -26.5 = 23.5 Reorder the terms: -26.5 + x = 23.5 Solving -26.5 + x = 23.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = 23.5 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 23.5 + 26.5 x = 23.5 + 26.5 Combine like terms: 23.5 + 26.5 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -26.5 = -23.5 Simplifying x + -26.5 = -23.5 Reorder the terms: -26.5 + x = -23.5 Solving -26.5 + x = -23.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = -23.5 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -23.5 + 26.5 x = -23.5 + 26.5 Combine like terms: -23.5 + 26.5 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, 3}
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